Numerical Analysis Group Research
Report NA-07/03
Solving large-scale quadratic eigenvalue problems with Hamiltonian eigenstructure using a structure-preserving Krylov subspace method
Peter Benner, Heike Faßbender and Martin Stoll
February 2007, 23 pages,
.pdf file
We consider the numerical solution of quadratic eigenproblems with spectra
that exhibit Hamiltonian symmetry. We propose to solve such problems
by applying a Krylov-Schur-type method based on the symplectic Lanczos
process to a structured linearization of the quadratic matrix polynomial. In
order to compute interior eigenvalues, we propose several shift-and-invert
operators with Hamiltonian structure. Our approach is tested for several
examples from structural analysis and gyroscopic systems.
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